There's two reasons that I can see why Trump would pardon/discuss pardoning Blagojevich.
Reason One:
Friendship/Relationship.
If Trump likes him and/or has some connection to him, friend of a friend. Pardoning a friend of a friend is easy enough to understand.
They met on celebrity apprentice but Trump says that beyond that, they don't really know each other and I think that's a fair statement. Both men were busy and lived in different parts of the country and there would have been little reason for them to maintain a relationship after the show. Trump, for example, seems to have made very relatively friends prior to his inserting himself into the political arena. There was Michael Cohen who's been a lawyer and business partner, but all his "friends" appear to be either business related or family. There's no reason to expect that he and Rod would have been close. Trump runs a family business.
People who work for law firms or big companies or wall street tend to work as part of a team and they know a lot of people. (I worked on Wall Street and I saw that as part of my Father's law firm. Lawyers have clients for example). Those kind of careers require meeting lots of people. Trump's business was more insular. There would have been little reason for him to have an extended relationship with Blagojevich even after they spent time doing a show together briefly. I tend towards believing Trump when he says that they met, but didn't maintain a relationship after doing the show together.
Reason two (and I think this is the more likely explanation).
Overzealous prosecutors and distraction.
Blagojevich reached out to Trump, so let's get that out of the way and Trump has said he would "consider" a pardon. He hasn't granted one. That's a key difference. If Trump is considering it, he can appear to be weighing the evidence. He can appear thoughtful. That's what "considering" implies.
Blagojevich has also been very critical of overzealous prosecution. He claims (incorrectly) to have been imprisoned for being stupid and saying things that many other politicians say. That's of course, bunk. Blagojevich did accept payments for state contracts and he didn't just say "this is a gold mine", he tried, more than once, to get something in return". But given that he's serving 14 years, and because a few other politicians have, occasionally been on the take* (citation needed), Blagojevich is seen by some as an example of overzealous prosecution, even if he's guilty, others who are just as guilty aren't serving time.
By considering Blagojevich's request, Trump touches on a couple things he likes. He exposes what is to some an example of overzealous prosecution against a politician and he appears thoughtful by considering something. It's a win for Trump to discuss the unfair treatment of Rod Blagojevich because it puts "unfair treatment" out there.
As to whether it's a win for him to issue the pardon, that's harder to say. Obviously some will cheer, others will boo, but we should cross that bridge when/if the pardon happens. For now, Trump gets something by saying he's considering it.
If I was to guess (and I know I shouldn't do that here, but I can't help myself because it's fun to guess what Trump will do). I think Trump will pardon him, but upon leaving office, not now. By putting it out now, but pardoning him in 2020 with a bunch of other pardons, then it's not a big surprise. If he pardons him soon, he opens himself up to both criticism as well as praise.
And let me add, while he was clearly guilty, Rod Blagojevich was also a first time offender and no more guilty than Bob Mcdonnell, who got off with being forced out of office and a scolding from the supreme court but no jail time. Bob was smarter and he said in court that the gifts were given to his wife, but I think it's fair to say that he was equally guilty.
I always thought that the 14 year sentence was too harsh. I realize that might be unnecessary commentary but since I hammered down the point that Blagojevich was guilty, I wanted to add this. 14 years is a lot.
